Answer:
10 and 19
Step-by-step explanation:
- In Algebra, an even number = 2x, because anything multiplied by 2 is even.
- There are two numbers in the question, I'll define the first one as 2x
- the other number is 1 less than twice of the first, so I'm going to define it <u>in algebra as 2(2x) - 1</u>, which is just 4x - 1
- the square of the first is

- the square of the second is

- add them together:

- this equation = 461, so

- simplify to

- I wont explain how to solve this here, since it is very complicated, if you don't know search up solving quadratics.
- the <u>solutions are 5 or -4.6</u>, it cannot be -4.6 since the question says positive, so the solution for <u>x = 5</u>
- substitute x into our equations for the two numbers in steps 1 and 2
- the <u>first number = 10, the second = 19</u>
Answer:
90
Step-by-step explanation:
Answer:
4.25
Step-by-step explanation:
We have that
f(x) = –4x²<span> + 24x + 13
</span>
we know that
The vertex form for a parabola that opens up or down is:
f(x) = a(x - h)^2 + k
in the given equation, <span>a=-4</span><span>, therefore we add zero to the original equation in the form of </span><span>4h</span>²<span>−4h</span>²
f(x) = –4x² + 24x + 4h²−4h² +13
<span>Factor 4 out of the first 3 terms and group them
</span>f(x) = –4*(x² -6x +h²) +4h² +13
<span>We can find the value of h by setting the middle term equal to -2hx
</span>−2hx=−6x
<span>h=3</span><span> and </span><span>4h</span>²<span>=<span>36
</span></span>f(x) = –4*(x² -6x +9) +36 +13
we know that the term (x² -6x +9) is equals to------> (x-3)²
so
f(x) = –4*(x-3)² +49
the answer isf(x) = –4*(x-3)² +49